Approximate solutions for the inextensible Heisenberg antiferromagnetic flow and solitonic magnetic flux surfaces in the normal direction in Minkowski space

2-s2.0-85102794313Motivated by recent researches in magnetic curves and their flows in different types of geometric manifolds and physical spacetime structures, we compute fractional Lorentz force equations associated with the magnetic n-lines in the normal direction in Minkowski space. Fractional evolution equations of magnetic n-lines due to inextensible Heisenberg antiferromagnetic flow are computed to construct the soliton surface associated with the inextensible Heisenberg antiferromagnetic flow. Then, their approximate solutions are investigated in terms of magnetic and geometric quantities via the conformable fractional derivative method. By considering arc-length and time-dependent orthogonal curvilinear coordinates, we finally determine the necessary and sufficient conditions that have to be satisfied by these quantities to define the Lorentz magnetic flux surfaces based on the inextensible Heisenberg antiferromagnetic flow model in Minkowski space. © 2021 Elsevier Gmb

Soliton propagation of electromagnetic field vectors of polarized light ray traveling in a coiled optical fiber in Minkowski space with Bishop equations

Abstract: In this paper, we firstly obtain the evolution equations of the magnetic field and electric field vectors of polarized light ray propagating along a coiled optical fiber in Minkowski space. Then we define new kinds of binormal motions and new kinds of Hasimoto transformations to relate these evolution equations into the nonlinear Schrodinger’s equation. During this procedure, we use a parallel adapted frame or more commonly known as Bishop frame to characterize the coiled optical fiber geometrically. We also propose perturbed solutions of the nonlinear Schrödinger’s evolution equation that governs the propagation of solitons through the electric field (E) and magnetic field (M) vectors. Finally, we provide some numerical simulations to supplement the analytical outcomes. Graphical abstract: [Figure not available: see fulltext.]. © 2019, EDP Sciences / Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature

Biswas-Milovic model and its optical solitons

International Conference on Numerical Analysis and Applied Mathematics 2018, ICNAAM 2018 -- 13 September 2018 through 18 September 2018 -- -- 149843In this work, optical solitons are obtained for the Biswas - Milovic equation as a generalized model via the extended generalizing Riccati mapping method. This method reveals several optical solitons including traveling wave solutions. The found solutions are identified with two different forms including the hyperbolic functions, the rational functions and the trigonometric functions. Reliability of our solution is given graphical consequens. © 2019 Author(s)

Some new exact solutions for derivative nonlinear Schrödinger equation with the quintic non-Kerr nonlinearity

The extended generalizing Riccati mapping method (EGRM) is used to solve the derivative nonlinear Schrödinger equation (DNLSe) with the dimensionless shape. This method reveals several optical solitons including traveling wave solutions (TWS). The studied solutions are identified in four different families including the hyperbolic, the rational and the trigonometric functions. Evaluations of the method are presented with graphical results obtained from our solutions. © 2020 World Scientific Publishing Company

New optical solitons for Biswas–Arshed equation with higher order dispersions and full nonlinearity

In this paper, the extended Jacobi's elliptic function approach is used to solve the Biswas–Arshed equation in two different types. This method reveals several optical solitons including traveling wave solutions. The found solutions are identified bright, dark, singular optical solitons and Jacobi elliptic function solutions. Reliability of the process is presented with graphical consequence of derived solutions. © 2019 Elsevier Gmb